Mario Monti, Italy’s outgoing Prime Minister and leader of a centrist coalition for early elections in February.

The question is clear, and has evidently crossed the minds of some of the country’s political leaders.

One view is that some kind of coalition government will be cobbled together but it won’t last long.

“I have the impression that the next legislature won’t last very long,” Pier Ferdinando Casini, head of the centrist UDC party, said recently.

Mr. Casini is the chief political ally of the outgoing Prime Minister Mario Monti, a technocrat who has decided to seek power again but with an electoral mandate. The new centrist grouping is polling around 15%, making it a potential spoiler for the center-left coalition expected to win by far the most votes but perhaps not a majority of seats in both chambers.

But there’s another possibility – that the vote really has no result.

“Who knows, perhaps in a couple of months I’ll still be sitting right here,” Fabrizio Barca, the minister for regional development in Mr. Monti’s cabinet, said in a recent interview with a local newspaper.

Mr. Barca is not running for election and is not even a member of a party – although he is openly seeking a leadership position in one of Italy’s left-leaning movements.

What his words implied was that if no government can be formed after the polls close, the current one will remain in office on a caretaker basis.

In Italy, the head of state — the president of the republic — must swear in governments once convinced they have a viable shelf life in the form of bicameral majorities.

In this case, President Giorgio Napolitano — who in late 2011 brokered Mr. Monti’s arrival on the scene and his broad-based emergency majority — is not keen to perform any more political pyrotechnics. His term ends in May, meaning Parliament will elect his successor before then. Moreover he’s 87 years old.

That’s a bit of a conundrum. Newly-elected lawmakers with no functional government may be called upon to vote for a new head of state while basically expecting to head back to the ballot box.

Picking the head of state usually entails subtle and even arcane compromises, which will be hard to find if political uncertainty is high. Indeed, it might prove hard to agree on any presidential name other than Mr. Napolitano himself.

“I’d vote for Napolitano,” Mr. Monti himself said this week, underscoring how the no-winner scenario is occupying the thoughts of the country’s main players.

The shock solution, presumably, would be for Mr. Napolitano to accept a second seven-year term and pilot the country through another electoral process fairly soon.

If he then chose to resign in 2014, when he will turn 89, the Rubik’s Cube of Italian politics could even extend to Brussels and Frankfurt.